Hyperkähler歧管的极限混合Hodge结构

Pub Date : 2018-07-11 DOI:10.17323/1609-4514-2020-2-423-436

A. Soldatenkov

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引用次数: 12

摘要

本注释的灵感来自Deligne关于Hodge结构在无穷远处的局部行为的工作。我们研究了紧致超k“ahler流形退化族的极限混合Hodge结构。我们证明了当$H^2$上的单调作用具有最大单势指数时，所有上同调群上的极限混合Hodge结构都是Hodge-Tate型的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Limit Mixed Hodge Structures of Hyperkähler Manifolds

This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. We study limit mixed Hodge structures of degenerating families of compact hyperk\"ahler manifolds. We show that when the monodromy action on $H^2$ has maximal index of unipotency, the limit mixed Hodge structures on all cohomology groups are of Hodge-Tate type.

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